The result shows that the real and imaginary parts of the square root of any complex number a+i⁢b can be obtained from the real part a and imaginary part b of the number by using only algebraic operations, i.e. the rationaloperations and the . Apparently, the same is true for all roots of a complex number with index (http://planetmath.org/NthRoot) an integer power of 2.

In practise, when determining the square root of a non-real complex number, one need not to remember the (2), but it’s better to solve concretely the equation (1).